Khả Năng p-Affine Tái Nghiên Cứu

Federer, H., Ziemer, W.P.: The Lebesgue set of a function whose distribution derivatives are \(p\)-th power summable. Indiana Univ. Math. J. 22, 139–158 (1971) Gardner, R.J., Hartenstine, D.: Capacities, surface area, and radial sums. Adv. Math. 221, 601–625 (2009) Heinonen, J., Kilpeläinen, T., Martio, O.: Nonlinear Potential Theory of Degenerate Elliptic Equations. Oxford University Press, Oxford (1993) Kubota, T.: Uber die konvex-geschlossenen Mannigfaltigkeiten im n-dimensionalen Raume. Sci. Rep. Tojoku Univ. 14, 85–99 (1925) Ludwig, M., Xiao, J., Zhang, G.: Sharp convex Lorentz-Sobolev inequalities. Math. Ann. 350, 169–197 (2011) Lutwak, E.: The Brunn-Minkowski-Firey theory I: mixed volumes and the Minkowski problem. J. Differ. Geom. 38, 131–150 (1993) Lutwak, E.: The Brunn-Minkowski-Firey theory II: affine and geominimal surface areas. Adv. Math. 118, 244–294 (1996) Lutwak, E., Yang, D., Zhang, G.: \(L_p\) affine isoperimetric inequalities. J. Differ. Geom. 56, 111–132 (2000) Lutwak, E., Yang, D., Zhang, G.: Sharp affine \(L_p\) Sobolev inequalities. J. Differ. Geom. 62, 17–38 (2002) Maz’ya, V.: Sobolev Spaces with Applications to Elliptic Partial Differential Equations, 2nd, revised and augmented edition. Springer, New York (2011) Petty, C.M.: Isoperimetric problems. In: Proceedings of the Conference on Convexity and Combinatorial Geometry (Univ. Oklahoma, 1971), pp. 26–41. University of Oklahoma, Norman (1972) Schneider, R.: Convex bodies: the Brunn-Minkowski theory. In: Encyclopedia of Mathematics and its Applications, vol. 44. Cambridge University Press, Cambridge (1993) Troyanov, M.: Parabolicity of manifolds. Siberian Adv. Math. 9, 125–150 (1999) Xiao, J.: The sharp Sobolev and isoperimetric inequalities split twice. Adv. Math. 211, 417–435 (2007). Corrigendum. Adv. Math. 268, 906–914 (2015) Xiao, J.: The \(p\)-affine capacity. J. Geom. Anal. 26, 947–966 (2016) Xiao, J.: A maximum problem of S.-T. Yau for variational \(p\)-capacity. Adv. Geom. (2016) in press Xiao, J., Zhang, N.: The relative \(p\)-affine capacity. Proc. Am. Math. Soc. 144, 3537–3554 (2016) Xu, X.: Some results on functional capacity and their applications to \(p\)-Laplacian problems involving measure data. Nonlinear Anal. 27, 17–36 (1996) Zhang, G.: The affine Sobolev inequality. J. Differ. Geom. 53, 183–202 (1999)